Does this translate as, "The mayor of the bloody and savage city of Juarez Mexico was afraid that the deaths of the sixteen youths had happened rashly [mistakenly?]"? If the city is bloody and savage, it would be "cruentae saevaeque urbis." I'm unsure what the mayor fears in the last clause, but if "mortes" is the subject, then the verb needs to be plural. If "sedecim adulescentum" is genitive, it needs to be "adulescentium." If the youths were mistakenly killed (because the cartel meant to target someone else), then you could say "timuit ne sedecim adulescentium perperam/sine ratione interfecti fuissent." (Whitaker's lists "encaenium" and "exenium" as adverbs meaning "by mistake," but I've never ever seen these, and they don't seem to be in Lewis & Short...)

"The government is offering a large monetary reward to any citizen who can perhaps(?) reveal the murderers." Not sure what to do with feliciter here, which means "happily." Willingly? Voluntarily? Then you'd want something like "sua sponte."

Good work! Just need to work on more natural phrasing in parts. I'm sure others can recommend much more felicitous phrasing and vocabulary than I've indicated. Terrible news by the way. It's tragic that so many people are killed unjustly all over the world...

I used "temere" because I was looking for the word "randomly" which is the word the article used. The Collins dictionary I have gave me "temere" for "at random."

It seems the mayor is stating that the killing wasn't even a case of mistaken identity, but just plain random. There was a party, they rolled up, they killed everybody.

"timuit ne sedecim adulescentium perperam/sine ratione interfecti fuissent." Got it. However, I was trying to use indirect speech with an accusative subject, and that's why I used "mortes" and "fuisse." However, it appears that with verbs of FEARING, the SUBJUNTIVE MUST BE USED, is that correct?

Collins gave me "feliciter." I was looking for "successfully" going from English-Latin and that's the word it gave me, along with "prospere" and "bene."

I used "temere" because I was looking for the word "randomly" which is the word the article used. The Collins dictionary I have gave me "temere" for "at random."

It seems the mayor is stating that the killing wasn't even a case of mistaken identity, but just plain random. There was a party, they rolled up, they killed everybody.

You're right, "temere" can mean "at random," which I overlooked. Other options might be casu and fortuito.

"timuit ne sedecim adulescentium perperam/sine ratione interfecti fuissent." Got it. However, I was trying to use indirect speech with an accusative subject, and that's why I used "mortes" and "fuisse." However, it appears that with verbs of FEARING, the SUBJUNTIVE MUST BE USED, is that correct?

Correct, clauses of fearing require the subjunctive. It's like with an ut-purpose clause, except that it's with ne. Sometimes clauses of fearing are explained as two separate sentences, like "timeo ne canes me mordeant" "I'm afraid that the dogs will bite me/lest the dogs bite me." This could be rendered "timeo! I'm afraid!" "ne canes me mordeant Don't let the dogs bite me!" The ne + subjunctive is by itself a kind of "don't let this happen" meaning. This is a good way to get your head around clauses of fearing that have ut instead of ne (relatively rare). If you had "timeo ut canes me mordeant" it would mean "I'm afraid that the dogs WON'T bite me." In other words, you are afraid that something won't happen (versus that something WILL happen with a NE clause). A better example might be "timeo ut veniat! I'm afraid that he won't come." Breaking this into two sentences you get "Timeo! I'm afraid! Ut veniat That he come!/Let him come!" More than you probably needed, but there you go.

Collins gave me "feliciter." I was looking for "successfully" going from English-Latin and that's the word it gave me, along with "prospere" and "bene."

Nescio quid velis dicere per "Cum domum inlicta esset, astutissime Fidler..."I don't know what you mean by that phrase. I guessed "Pretending the house was derelict, very cleverly Fidler..." "Pretending dereliction, very cleverly Fidler..."